Wiggins was dropped by the main pack in the last hour of a rain lashed stage 12 on Thursday and finished three minutes and 17 seconds back on winner and compatriot Mark Cavendish.
Overall the multiple Olympic gold medallist and pre-race favourite dropped to 13th, 5:22 down on Italian leader Vincenzo Nibali.
Team Sky team principal Sir Dave Brailsford said: “We monitored Bradley overnight and this morning we’ve withdrawn him from the Giro after consulting the team doctor. His chest infection has been getting worse and our primary concern is always the health of our riders.
“Bradley will return to the UK today for treatment and to rest and we hope to have him back on the road as soon as possible.
“As a passionate racer he wanted to continue but he is simply unable to do so on medical grounds.”
The Giro had been this season's major goal for Wiggins but the 33-year-old has suffered a run of bad luck since the race began in Naples on May 4, including a downhill crash, missing out on a time trial win because of a puncture and now illness.
"I think he's brave and showed a lot of courage to get on his bike. When you open the curtains and are feeling as sick as he was, the last thing you want to see is the pouring rain," Brailsford said on Thursday of Wiggins who has been taking antibiotics for the last few days.
"We all had colds and the flu and we all know how he feels. I'm sure some of us would call in sick and have a day off, but these guys can't do that."
Despite Wiggins's misfortune, Team Sky are still in the fight for the overall classification, with Colombian rider Rigoberto Uran lying third overall, 2:04 behind leader Nibali.
"He looks in good shape and so for us it's still a very exciting race and we'll try to get on the podium or even better with Rigoberto," said Brailsford.
The Giro d'Italia finishes in Brescia on May 26.
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- Dave Brailsford